generated ideal
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Ideal (ring theory) — In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. The ideal concept allows the generalization in an appropriate way of some important properties of integers like even number or multiple of 3 . For instance, in… … Wikipedia
Ideal norm — In commutative algebra, the norm of an ideal is a generalization of a norm of an element in the field extension. It is particularly important in number theory since it measures the size of an ideal of a complicated number ring in terms of an… … Wikipedia
Ideal class group — In mathematics, the extent to which unique factorization fails in the ring of integers of an algebraic number field (or more generally any Dedekind domain) can be described by a certain group known as an ideal class group (or class group). If… … Wikipedia
Ideal (order theory) — In mathematical order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring ideal of abstract algebra, it has subsequently been generalized to a different… … Wikipedia
Ideal triangle — In hyperbolic geometry an ideal triangle is a hyperbolic triangle whose three vertices all lie on the circle at infinity. In the Poincaré disk model an ideal triangle is bounded by three circles which intersect the boundary circle at right angles … Wikipedia
Finitely generated — may refer to: * finitely generated group * finitely generated abelian group * finitely generated module: in particular, finitely generated ideal * finitely generated algebra * finitely generated space … Wikipedia
Structure theorem for finitely generated modules over a principal ideal domain — In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that… … Wikipedia
Principal ideal domain — In abstract algebra, a principal ideal domain, or PID is an integral domain in which every ideal is principal, i.e., can be generated by a single element.Principal ideal domains are thus mathematical objects which behave somewhat like the… … Wikipedia
Finitely-generated module — In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated R module also may be called a finite R module or finite over R.[1] Related concepts include finitely cogenerated modules, finitely… … Wikipedia
Principal ideal — In ring theory, a branch of abstract algebra, a principal ideal is an ideal I in a ring R that is generated by a single element a of R .More specifically: * a left principal ideal of R is a subset of R of the form R a := { r a : r in R }; * a… … Wikipedia
Prime ideal — In mathematics, a prime ideal is a subset of a ring which shares many important properties of a prime number in the ring of integers. This article only covers ideals of ring theory. Prime ideals in order theory are treated in the article on… … Wikipedia
